(Updates prices, adds quotes, changes byline, changes headline, changes dateline from previous PARIS/KUALA LUMPUR )

MEXICO CITY, March 27 (Reuters) - Chicago corn futures were down on Monday, retreating from a more than three-week high in the previous session, and wheat edged higher on earlier short covering and uncertainty over Black Sea exports.

Soybeans edged higher, supported by a jump in soybean oil prices.

Private exporters reported the sale of 112,800 tonnes of corn to unknown destinations, the U.S. Agriculture Department said.

After last week's heavy Chinese demand, corn was slipping as traders speculated on weather conditions and planting timings for the new crops, analysts said.

"It's all old crop versus new crop. Last week when old crop corn was rallying, new crop corn wasn't doing anything. This is a little bit of correction," said Tom Fritz, a partner with EFG Group in Chicago.

The most active corn contract on the Chicago Board of Trade (CBOT) slipped 0.31% to $6.41 a bushel by 1021 CDT (1521 GMT).

Wheat was up 0.91% to $6.94-3/4 a bushel and soybeans rose 0.47% to $14.35 a bushel.

"It's the hard varieties (of wheat) that are leading the way," Fritz added. "Kansas City wheat has a legitimate story with the dryness in the southern plains, and spring wheat has a legitimate story about the lack of snow melt."

Traders are also assessing uncertainties over the Black Sea grains deal after Russian business newspaper Vedomosti on Friday reported that Moscow could recommend a temporary halt in wheat and sunflower exports.

Sources later told Reuters that Russia had no plans to halt wheat exports but wanted exporters to ensure prices paid to farmers were high enough to cover average production costs. (Reporting by Cassandra Garrison in Mexico City, Mei Mei Chu and Rajendra Jadhav in Kuala Lumpur, Sybille de La Hamaide in Paris; Editing by Subhranshu Sahu, Sonia Cheema, David Goodman anad Alison Williams)